I always fit new pads with new discs on road going motors.
New discs and pads need to be conditioned for use which is why you have a bedding in procedure. This is not just for 'shaping' the pads to the disc but to put down an even transfer of pad material onto the discs and to heat cycle the pads to remove resins left over from the manufacturing process.
If you fit old, unevenly worn pads to a fresh disc then the transfer of material will also be uneven potentially leading to hot spotting, poor braking performance and disc imbalance and possibly ruining the new disc (see Juddering below).
Fitting new pads to old discs you do not have so much of an issue as long as the disc has worn evenly. It will already have the transfer of pad material over the whole disc surface from the old pads and the new pads can wear to the surface without issue although they will still need to be bedded in.
The best resource for braking information is here: http://www.stoptech.com/technical-support/technical-white-papers
A) Juddering under braking is often put down to 'warped' discs however true 'warping' is actually pretty rare. What actually happens instead is pad material is deposited unevenly onto the disc leading to hot spotting and an imbalance in the disc and therefore the juddering. If the discs are not damaged (check for cracks) the fix is often just a case of re-bedding in the pads to the disc which can remove high spots of pad material if caught early enough. If the problems still persists and the braking system is checked, cleaned and is operating correctly then the disc runout needs to be measured. Discs can be skimmed back to a flat fresh face if there's enough thickness left in them although in bad cases the hot spots may effect the discs to a deep depth in which case the discs need replacing.
B) I would fit new pads.
Brakes, tyres and suspension are the most important safety components on any car other than the 'nut' behind the wheel. It's not worth compromising to save a few pounds.
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